How many questions are in this quiz?

This topic quiz currently has 150 active questions from the selected topic.

Is there a timer in this quiz?

Yes, the timer uses 35 seconds per question for Medium difficulty and shows the total remaining time on the page.

Can I open each question separately?

Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.

Mathematics Quiz - Class 11 Mathematics Permutations And...

Question 1/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{(n+1)!}{n!}=8), तो (n) का मान क्या है?

If (\frac{(n+1)!}{n!}=8), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.

Step 2

Why this answer is correct

The correct answer is B. (7). (\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.

Step 3

Exam Tip

(\frac{(n+1)!}{n!}=n+1), इसलिए (n+1=8) और (n=7)। पहले फैक्टोरियल अनुपात सरल करें।

Open Question Page

Question 2/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{9!}{7!}-5!\) का मान क्या है?

What is the value of \(\frac{9!}{7!}-5!\)?

Explanation opens after your attempt

Correct Answer

A. (-48)

Step 1

Concept

\(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.

Step 2

Why this answer is correct

The correct answer is A. (-48). \(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.

Step 3

Exam Tip

\(\frac{9!}{7!}=9\times8=72\) और (5!=120), इसलिए मान (-48) है। घटाव में चिह्न ध्यान से रखें।

Open Question Page

Question 3/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (n=3), तो (\frac{(n+2)!}{n!}) का मान क्या होगा?

If (n=3), what will be the value of (\frac{(n+2)!}{n!})?

Explanation opens after your attempt

Correct Answer

B. (20)

Step 1

Concept

Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.

Step 2

Why this answer is correct

The correct answer is B. (20). Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.

Step 3

Exam Tip

(n=3) रखने पर \(\frac{5!}{3!}=5\times4=20\)। पहले चर का मान रखें।

Open Question Page

Question 4/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि ((n+1)!=720), तो (n) का मान क्या है?

If ((n+1)!=720), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.

Step 2

Why this answer is correct

The correct answer is B. (5). Since (720=6!), (n+1=6) and (n=5). Remember small factorial values.

Step 3

Exam Tip

(720=6!), इसलिए (n+1=6) और (n=5)। छोटे फैक्टोरियल मान याद रखें।

Open Question Page

Question 5/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{6!}{3!}+4!\) का मान क्या है?

What is the value of \(\frac{6!}{3!}+4!\)?

Explanation opens after your attempt

Correct Answer

C. (144)

Step 1

Concept

\(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.

Step 2

Why this answer is correct

The correct answer is C. (144). \(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.

Step 3

Exam Tip

\(\frac{6!}{3!}=120\) और (4!=24), इसलिए कुल (144) है। पहले भिन्न को सरल करें।

Open Question Page

Question 6/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{5!}{3!}+\frac{5!}{4!}\) का मान क्या है?

What is the value of \(\frac{5!}{3!}+\frac{5!}{4!}\)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

\(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.

Step 2

Why this answer is correct

The correct answer is B. (25). \(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.

Step 3

Exam Tip

\(\frac{5!}{3!}=20\) और \(\frac{5!}{4!}=5\), इसलिए योग (25) है। हर अनुपात अलग-अलग सरल करें।

Open Question Page

Question 7/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!}) का सरल मान क्या है?

What is the simplified value of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).

Step 2

Why this answer is correct

The correct answer is B. (2). The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).

Step 3

Exam Tip

पहला अनुपात (n+2) और दूसरा (n) है। अंतर ((n+2)-n=2) होगा।

Open Question Page

Question 8/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\) का मान क्या है?

What is the value of \(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (71)

Step 1

Concept

\(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.

Step 2

Why this answer is correct

The correct answer is C. (71). \(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.

Step 3

Exam Tip

\(\frac{8!}{5!,3!}=56\) और \(\frac{6!}{4!,2!}=15\), इसलिए कुल (71) है। दोनों पदों को अलग हल करें।

Open Question Page

Question 9/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{n!}{(n-2)!}=42), तो (n) का मान क्या है?

If (\frac{n!}{(n-2)!}=42), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).

Step 2

Why this answer is correct

The correct answer is B. (7). (\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).

Step 3

Exam Tip

(\frac{n!}{(n-2)!}=n(n-1)), इसलिए (n(n-1)=42)। \(7\times6=42\), अतः (n=7)।

Open Question Page

Question 10/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{10!}{8!}+\frac{4!}{2!}\) का मान क्या है?

What is the value of \(\frac{10!}{8!}+\frac{4!}{2!}\)?

Explanation opens after your attempt

Correct Answer

C. (102)

Step 1

Concept

\(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.

Step 2

Why this answer is correct

The correct answer is C. (102). \(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.

Step 3

Exam Tip

\(\frac{10!}{8!}=90\) और \(\frac{4!}{2!}=12\), इसलिए योग (102) है। समान फैक्टोरियल भाग काटें।

Open Question Page

Question 11/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{7!-6!}{6!}\) का मान क्या है?

What is the value of \(\frac{7!-6!}{6!}\)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.

Step 2

Why this answer is correct

The correct answer is B. (6). Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.

Step 3

Exam Tip

\(7!=7\times6!\), इसलिए (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6)। समान फैक्टोरियल बाहर लें।

Open Question Page

Question 12/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+3)!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+3)!}{n!})?

Explanation opens after your attempt

Correct Answer

A. ((n+3)(n+2)(n+1))

Step 1

Concept

((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is A. ((n+3)(n+2)(n+1)). ((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.

Step 3

Exam Tip

((n+3)!=(n+3)(n+2)(n+1)n!), इसलिए (n!) कट जाता है। क्रम से तीन गुणक बचते हैं।

Open Question Page

Question 13/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{(n+2)!}{n!}=30), तो (n) का मान क्या है?

If (\frac{(n+2)!}{n!}=30), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

(\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). (\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).

Step 3

Exam Tip

(\frac{(n+2)!}{n!}=(n+2)(n+1))। \(6\times5=30\), इसलिए (n=4)।

Open Question Page

Question 14/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\) का मान क्या है?

What is the value of \(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\)?

Explanation opens after your attempt

Correct Answer

A. (63)

Step 1

Concept

\(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.

Step 2

Why this answer is correct

The correct answer is A. (63). \(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.

Step 3

Exam Tip

\(\frac{9!}{6!,3!}=84\) और \(\frac{7!}{5!,2!}=21\), इसलिए अंतर (63) है। दोनों संयोजन-जैसे पद अलग निकालें।

Open Question Page

Question 15/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{5!+3!}{4!}\) का मान क्या है?

What is the value of \(\frac{5!+3!}{4!}\)?

Explanation opens after your attempt

Correct Answer

C. \(\frac{21}{4}\)

Step 1

Concept

The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).

Step 2

Why this answer is correct

The correct answer is C. \(\frac{21}{4}\). The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).

Step 3

Exam Tip

अंश (120+6=126) है और (4!=24)। इसलिए मान \(\frac{126}{24}=\frac{21}{4}\) है।

Open Question Page

Question 16/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{8!}{4!}-\frac{7!}{4!}\) का मान क्या है?

What is the value of \(\frac{8!}{4!}-\frac{7!}{4!}\)?

Explanation opens after your attempt

Correct Answer

B. (1470)

Step 1

Concept

(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.

Step 2

Why this answer is correct

The correct answer is B. (1470). (\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.

Step 3

Exam Tip

(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470)। समान हर होने पर अंश मिलाकर देखें।

Open Question Page

Question 17/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{11!}{9!,2!}\) का मान क्या है?

What is the value of \(\frac{11!}{9!,2!}\)?

Explanation opens after your attempt

Correct Answer

B. (55)

Step 1

Concept

\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).

Step 2

Why this answer is correct

The correct answer is B. (55). \(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).

Step 3

Exam Tip

\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\)। बड़े फैक्टोरियल को (9!) तक लिखें।

Open Question Page

Question 18/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

कौन सा रूप \(\frac{12!}{9!}\) के बराबर है?

Which expression is equal to \(\frac{12!}{9!}\)?

Explanation opens after your attempt

Correct Answer

B. \(12\times11\times10\)

Step 1

Concept

\(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.

Step 2

Why this answer is correct

The correct answer is B. \(12\times11\times10\). \(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.

Step 3

Exam Tip

\(\frac{12!}{9!}=12\times11\times10\)। हर में (9!) होने से (9!) तक का भाग कट जाता है।

Open Question Page

Question 19/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+1)!-n!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+1)!-n!}{n!})?

Explanation opens after your attempt

Correct Answer

B. (n)

Step 1

Concept

Since ((n+1)!=(n+1)n!), the numerator is (n!{(n+1)-1}=nn!). Dividing gives (n).

Step 2

Why this answer is correct

The correct answer is B. (n). Since ((n+1)!=(n+1)n!), the numerator is (n!{(n+1)-1}=nn!). Dividing gives (n).

Step 3

Exam Tip

((n+1)!=(n+1)n!), इसलिए अंश (n!{(n+1)-1}=nn!) है। भाग देने पर (n) मिलता है।

Open Question Page

Question 20/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{n!}{(n-1)!}+2=9), तो (n) का मान क्या है?

If (\frac{n!}{(n-1)!}+2=9), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

(\frac{n!}{(n-1)!}=n), so (n+2=9). Therefore, (n=7).

Step 2

Why this answer is correct

The correct answer is C. (7). (\frac{n!}{(n-1)!}=n), so (n+2=9). Therefore, (n=7).

Step 3

Exam Tip

(\frac{n!}{(n-1)!}=n), इसलिए (n+2=9)। अतः (n=7) है।

Open Question Page

Question 21/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{6!}{2!,4!}+\frac{5!}{2!,3!}\) का मान क्या है?

What is the value of \(\frac{6!}{2!,4!}+\frac{5!}{2!,3!}\)?

Explanation opens after your attempt

Correct Answer

B. (25)

Step 1

Concept

\(\frac{6!}{2!,4!}=15\) and \(\frac{5!}{2!,3!}=10\), so the total is (25). Count the smaller terms separately.

Step 2

Why this answer is correct

The correct answer is B. (25). \(\frac{6!}{2!,4!}=15\) and \(\frac{5!}{2!,3!}=10\), so the total is (25). Count the smaller terms separately.

Step 3

Exam Tip

\(\frac{6!}{2!,4!}=15\) और \(\frac{5!}{2!,3!}=10\), इसलिए कुल (25) है। छोटे पदों को अलग-अलग गिनें।

Open Question Page

Question 22/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{7!}{3!,4!}\times2!\) का मान क्या है?

What is the value of \(\frac{7!}{3!,4!}\times2!\)?

Explanation opens after your attempt

Correct Answer

B. (70)

Step 1

Concept

\(\frac{7!}{3!,4!}=35\) and (2!=2), so the product is (70). Simplify the fraction first.

Step 2

Why this answer is correct

The correct answer is B. (70). \(\frac{7!}{3!,4!}=35\) and (2!=2), so the product is (70). Simplify the fraction first.

Step 3

Exam Tip

\(\frac{7!}{3!,4!}=35\) और (2!=2), इसलिए गुणनफल (70) है। पहले भिन्न को सरल करें।

Open Question Page

Question 23/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{10!-9!}{8!}\) का मान क्या है?

What is the value of \(\frac{10!-9!}{8!}\)?

Explanation opens after your attempt

Correct Answer

B. (81)

Step 1

Concept

The numerator is (9!(10-1)=9\cdot9!). Thus \(\frac{9\cdot9!}{8!}=9\times9=81\).

Step 2

Why this answer is correct

The correct answer is B. (81). The numerator is (9!(10-1)=9\cdot9!). Thus \(\frac{9\cdot9!}{8!}=9\times9=81\).

Step 3

Exam Tip

अंश (9!(10-1)=9\cdot9!) है। \(\frac{9\cdot9!}{8!}=9\times9=81\) मिलता है।

Open Question Page

Question 24/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+2)!-(n+1)!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!-(n+1)!}{n!})?

Explanation opens after your attempt

Correct Answer

A. ((n+1)²)

Step 1

Concept

The numerator is ((n+1)![(n+2)-1]=(n+1)²n!). After cancelling (n!), the result is ((n+1)²).

Step 2

Why this answer is correct

The correct answer is A. ((n+1)²). The numerator is ((n+1)![(n+2)-1]=(n+1)²n!). After cancelling (n!), the result is ((n+1)²).

Step 3

Exam Tip

अंश ((n+1)![(n+2)-1]=(n+1)²n!) है। (n!) कटने पर ((n+1)²) मिलता है।

Open Question Page

Question 25/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{(n+3)!}{(n+1)!}=56), तो (n) का मान क्या है?

If (\frac{(n+3)!}{(n+1)!}=56), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(8\times7=56\), (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(8\times7=56\), (n=5).

Step 3

Exam Tip

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(8\times7=56\), इसलिए (n=5)।

Open Question Page

Question 26/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{5!,3!}{4!}\) का मान क्या है?

What is the value of \(\frac{5!,3!}{4!}\)?

Explanation opens after your attempt

Correct Answer

B. (30)

Step 1

Concept

\(\frac{5!}{4!}=5\) and (3!=6), so the value is (30). Simplify multiplication and division step by step.

Step 2

Why this answer is correct

The correct answer is B. (30). \(\frac{5!}{4!}=5\) and (3!=6), so the value is (30). Simplify multiplication and division step by step.

Step 3

Exam Tip

\(\frac{5!}{4!}=5\) और (3!=6), इसलिए मान (30) है। गुणन और भाग को क्रम से सरल करें।

Open Question Page

Question 27/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{8!}{7!}+\frac{7!}{6!}+\frac{6!}{5!}\) का मान क्या है?

What is the value of \(\frac{8!}{7!}+\frac{7!}{6!}+\frac{6!}{5!}\)?

Explanation opens after your attempt

Correct Answer

C. (21)

Step 1

Concept

The three terms are (8), (7), and (6) respectively. The sum is (8+7+6=21).

Step 2

Why this answer is correct

The correct answer is C. (21). The three terms are (8), (7), and (6) respectively. The sum is (8+7+6=21).

Step 3

Exam Tip

तीनों पद क्रमशः (8), (7) और (6) हैं। योग (8+7+6=21) है।

Open Question Page

Question 28/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{9!}{5!,4!}\div\frac{6!}{4!,2!}\) का मान क्या है?

What is the value of \(\frac{9!}{5!,4!}\div\frac{6!}{4!,2!}\)?

Explanation opens after your attempt

Correct Answer

B. \( \frac{42}{5}\)

Step 1

Concept

The first term is (126) and the second is (15). Thus \(\frac{126}{15}=\frac{42}{5}\).

Step 2

Why this answer is correct

The correct answer is B. \( \frac{42}{5}\). The first term is (126) and the second is (15). Thus \(\frac{126}{15}=\frac{42}{5}\).

Step 3

Exam Tip

पहला पद (126) और दूसरा (15) है। \(\frac{126}{15}=\frac{42}{5}\) मिलता है।

Open Question Page

Question 29/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+4)!}{(n+2)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+4)!}{(n+2)!})?

Explanation opens after your attempt

Correct Answer

A. ((n+4)(n+3))

Step 1

Concept

((n+4)!=(n+4)(n+3)(n+2)!). After cancelling ((n+2)!), ((n+4)(n+3)) remains.

Step 2

Why this answer is correct

The correct answer is A. ((n+4)(n+3)). ((n+4)!=(n+4)(n+3)(n+2)!). After cancelling ((n+2)!), ((n+4)(n+3)) remains.

Step 3

Exam Tip

((n+4)!=(n+4)(n+3)(n+2)!)। ((n+2)!) कटने पर ((n+4)(n+3)) बचता है।

Open Question Page

Question 30/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{n!}{(n-3)!}=120), तो (n) का मान क्या है?

If (\frac{n!}{(n-3)!}=120), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

(\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(6\times5\times4=120\), (n=6).

Step 2

Why this answer is correct

The correct answer is C. (6). (\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(6\times5\times4=120\), (n=6).

Step 3

Exam Tip

(\frac{n!}{(n-3)!}=n(n-1)(n-2))। \(6\times5\times4=120\), इसलिए (n=6)।

Open Question Page

Question 31/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{7!}{5!}-\frac{6!}{4!}\) का मान क्या है?

What is the value of \(\frac{7!}{5!}-\frac{6!}{4!}\)?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

\(\frac{7!}{5!}=42\) and \(\frac{6!}{4!}=30\), so the difference is (12). Evaluate smaller ratios directly.

Step 2

Why this answer is correct

The correct answer is A. (12). \(\frac{7!}{5!}=42\) and \(\frac{6!}{4!}=30\), so the difference is (12). Evaluate smaller ratios directly.

Step 3

Exam Tip

\(\frac{7!}{5!}=42\) और \(\frac{6!}{4!}=30\), इसलिए अंतर (12) है। छोटे अनुपात सीधे निकालें।

Open Question Page

Question 32/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{4!+5!}{3!}\) का मान क्या है?

What is the value of \(\frac{4!+5!}{3!}\)?

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

The numerator is (24+120=144) and (3!=6). Therefore, the value is (24).

Step 2

Why this answer is correct

The correct answer is B. (24). The numerator is (24+120=144) and (3!=6). Therefore, the value is (24).

Step 3

Exam Tip

अंश (24+120=144) है और (3!=6)। इसलिए मान (24) है।

Open Question Page

Question 33/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{12!}{10!,2!}-\frac{5!}{3!,2!}\) का मान क्या है?

What is the value of \(\frac{12!}{10!,2!}-\frac{5!}{3!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (56)

Step 1

Concept

\(\frac{12!}{10!,2!}=66\) and \(\frac{5!}{3!,2!}=10\), so the difference is (56). Keep the larger and smaller terms separate.

Step 2

Why this answer is correct

The correct answer is C. (56). \(\frac{12!}{10!,2!}=66\) and \(\frac{5!}{3!,2!}=10\), so the difference is (56). Keep the larger and smaller terms separate.

Step 3

Exam Tip

\(\frac{12!}{10!,2!}=66\) और \(\frac{5!}{3!,2!}=10\), इसलिए अंतर (56) है। बड़े और छोटे पद अलग रखें।

Open Question Page

Question 34/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (n(n-1)=72), तो (\frac{n!}{(n-2)!}) का मान क्या होगा?

If (n(n-1)=72), what will be the value of (\frac{n!}{(n-2)!})?

Explanation opens after your attempt

Correct Answer

B. (72)

Step 1

Concept

(\frac{n!}{(n-2)!}=n(n-1)). From the given condition, its value is (72).

Step 2

Why this answer is correct

The correct answer is B. (72). (\frac{n!}{(n-2)!}=n(n-1)). From the given condition, its value is (72).

Step 3

Exam Tip

(\frac{n!}{(n-2)!}=n(n-1))। दिए गए अनुसार इसका मान (72) है।

Open Question Page

Question 35/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{6!}{5!}\times\frac{5!}{3!}\) का मान क्या है?

What is the value of \(\frac{6!}{5!}\times\frac{5!}{3!}\)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

The first ratio is (6) and the second is \(5\times4=20\). The product is \(6\times20=120\).

Step 2

Why this answer is correct

The correct answer is C. (120). The first ratio is (6) and the second is \(5\times4=20\). The product is \(6\times20=120\).

Step 3

Exam Tip

पहला अनुपात (6) और दूसरा \(5\times4=20\) है। गुणनफल \(6\times20=120\) है।

Open Question Page

Question 36/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{10!}{7!,3!}\) का मान क्या है?

What is the value of \(\frac{10!}{7!,3!}\)?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

\(\frac{10!}{7!,3!}=\frac{10\times9\times8}{6}=120\). Do not forget that (3!=6).

Step 2

Why this answer is correct

The correct answer is C. (120). \(\frac{10!}{7!,3!}=\frac{10\times9\times8}{6}=120\). Do not forget that (3!=6).

Step 3

Exam Tip

\(\frac{10!}{7!,3!}=\frac{10\times9\times8}{6}=120\)। (3!=6) रखना न भूलें।

Open Question Page

Question 37/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{7!+5!}{6!}\) का मान क्या है?

What is the value of \(\frac{7!+5!}{6!}\)?

Explanation opens after your attempt

Correct Answer

A. \(7+\frac{1}{6}\)

Step 1

Concept

\(\frac{7!}{6!}=7\) and \(\frac{5!}{6!}=\frac{1}{6}\), so the value is \(7+\frac{1}{6}\). Divide each term by the denominator separately.

Step 2

Why this answer is correct

The correct answer is A. \(7+\frac{1}{6}\). \(\frac{7!}{6!}=7\) and \(\frac{5!}{6!}=\frac{1}{6}\), so the value is \(7+\frac{1}{6}\). Divide each term by the denominator separately.

Step 3

Exam Tip

\(\frac{7!}{6!}=7\) और \(\frac{5!}{6!}=\frac{1}{6}\), इसलिए मान \(7+\frac{1}{6}\) है। पदों को हर से अलग-अलग भाग दें।

Open Question Page

Question 38/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि \(a=\frac{8!}{6!}\) और (b=3!), तो (a-b) का मान क्या है?

If \(a=\frac{8!}{6!}\) and (b=3!), what is the value of (a-b)?

Explanation opens after your attempt

Correct Answer

B. (50)

Step 1

Concept

\(a=8\times7=56\) and (b=6), so (a-b=50). Find both values separately first.

Step 2

Why this answer is correct

The correct answer is B. (50). \(a=8\times7=56\) and (b=6), so (a-b=50). Find both values separately first.

Step 3

Exam Tip

\(a=8\times7=56\) और (b=6), इसलिए (a-b=50)। पहले दोनों मान अलग निकालें।

Open Question Page

Question 39/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+2)!}{(n-1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!}{(n-1)!})?

Explanation opens after your attempt

Correct Answer

A. ((n+2)(n+1)n)

Step 1

Concept

((n+2)!=(n+2)(n+1)n(n-1)!). Hence after cancelling ((n-1)!), three factors remain.

Step 2

Why this answer is correct

The correct answer is A. ((n+2)(n+1)n). ((n+2)!=(n+2)(n+1)n(n-1)!). Hence after cancelling ((n-1)!), three factors remain.

Step 3

Exam Tip

((n+2)!=(n+2)(n+1)n(n-1)!)। इसलिए ((n-1)!) कटने पर तीन गुणक बचते हैं।

Open Question Page

Question 40/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{9!}{8!}+\frac{8!}{7!}-\frac{7!}{6!}\) का मान क्या है?

What is the value of \(\frac{9!}{8!}+\frac{8!}{7!}-\frac{7!}{6!}\)?

Explanation opens after your attempt

Correct Answer

C. (10)

Step 1

Concept

The three ratios are (9), (8), and (7) respectively. Hence (9+8-7=10).

Step 2

Why this answer is correct

The correct answer is C. (10). The three ratios are (9), (8), and (7) respectively. Hence (9+8-7=10).

Step 3

Exam Tip

तीन अनुपात क्रमशः (9), (8) और (7) हैं। इसलिए (9+8-7=10) है।

Open Question Page

Question 41/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{(n+1)!}{(n-1)!}=20), तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-1)!}=20), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

This ratio is (n(n+1)). Since \(4\times5=20\), (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). This ratio is (n(n+1)). Since \(4\times5=20\), (n=4).

Step 3

Exam Tip

यह अनुपात (n(n+1)) है। \(4\times5=20\), इसलिए (n=4)।

Open Question Page

Question 42/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{8!}{6!}-\frac{5!}{4!}+2!\) का मान क्या है?

What is the value of \(\frac{8!}{6!}-\frac{5!}{4!}+2!\)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

\(\frac{8!}{6!}=56\), \(\frac{5!}{4!}=5\), and (2!=2). Thus (56-5+2=53).

Step 2

Why this answer is correct

The correct answer is C. (53). \(\frac{8!}{6!}=56\), \(\frac{5!}{4!}=5\), and (2!=2). Thus (56-5+2=53).

Step 3

Exam Tip

\(\frac{8!}{6!}=56\), \(\frac{5!}{4!}=5\) और (2!=2)। इसलिए (56-5+2=53) है।

Open Question Page

Question 43/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{7!}{4!,3!}+\frac{7!}{6!,1!}\) का मान क्या है?

What is the value of \(\frac{7!}{4!,3!}+\frac{7!}{6!,1!}\)?

Explanation opens after your attempt

Correct Answer

C. (42)

Step 1

Concept

The first term is (35) and the second term is (7). The total is (42).

Step 2

Why this answer is correct

The correct answer is C. (42). The first term is (35) and the second term is (7). The total is (42).

Step 3

Exam Tip

पहला पद (35) और दूसरा पद (7) है। कुल (42) मिलता है।

Open Question Page

Question 44/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+3)!}{n!}) में कुल कितने क्रमागत गुणक बचते हैं?

How many consecutive factors remain in (\frac{(n+3)!}{n!})?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

(\frac{(n+3)!}{n!}=(n+3)(n+2)(n+1)). Therefore, three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is B. (3). (\frac{(n+3)!}{n!}=(n+3)(n+2)(n+1)). Therefore, three consecutive factors remain.

Step 3

Exam Tip

(\frac{(n+3)!}{n!}=(n+3)(n+2)(n+1))। इसलिए तीन क्रमागत गुणक बचते हैं।

Open Question Page

Question 45/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि \(x=\frac{9!}{7!}\) और \(y=\frac{6!}{4!}\), तो \(\frac{x}{y}\) का मान क्या है?

If \(x=\frac{9!}{7!}\) and \(y=\frac{6!}{4!}\), what is the value of \(\frac{x}{y}\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{12}{5}\)

Step 1

Concept

(x=72) and (y=30), so \(\frac{x}{y}=\frac{72}{30}=\frac{12}{5}\). Simplify the ratio at the end.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{12}{5}\). (x=72) and (y=30), so \(\frac{x}{y}=\frac{72}{30}=\frac{12}{5}\). Simplify the ratio at the end.

Step 3

Exam Tip

(x=72) और (y=30), इसलिए \(\frac{x}{y}=\frac{72}{30}=\frac{12}{5}\)। अनुपात को अंत में सरल करें।

Open Question Page

Question 46/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+2)!}{n!}+\frac{(n+1)!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!}{n!}+\frac{(n+1)!}{n!})?

Explanation opens after your attempt

Correct Answer

A. ((n+1)(n+3))

Step 1

Concept

The first term is ((n+2)(n+1)) and the second is (n+1). Taking common ((n+1)) gives ((n+1)(n+3)).

Step 2

Why this answer is correct

The correct answer is A. ((n+1)(n+3)). The first term is ((n+2)(n+1)) and the second is (n+1). Taking common ((n+1)) gives ((n+1)(n+3)).

Step 3

Exam Tip

पहला पद ((n+2)(n+1)) और दूसरा (n+1) है। समान ((n+1)) लेने पर ((n+1)(n+3)) मिलता है।

Open Question Page

Question 47/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{13!}{11!}-\frac{10!}{8!}\) का मान क्या है?

What is the value of \(\frac{13!}{11!}-\frac{10!}{8!}\)?

Explanation opens after your attempt

Correct Answer

B. (66)

Step 1

Concept

\(\frac{13!}{11!}=13\times12=156\) and \(\frac{10!}{8!}=10\times9=90\), so the difference is (66). Simplify both factorial ratios separately first.

Step 2

Why this answer is correct

The correct answer is B. (66). \(\frac{13!}{11!}=13\times12=156\) and \(\frac{10!}{8!}=10\times9=90\), so the difference is (66). Simplify both factorial ratios separately first.

Step 3

Exam Tip

\(\frac{13!}{11!}=13\times12=156\) और \(\frac{10!}{8!}=10\times9=90\), इसलिए अंतर (66) है। पहले दोनों फैक्टोरियल अनुपात अलग-अलग सरल करें।

Open Question Page

Question 48/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

यदि (\frac{(n+2)!}{(n-1)!}=210), तो (n) का मान क्या है?

If (\frac{(n+2)!}{(n-1)!}=210), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(\frac{(n+2)!}{(n-1)!}=(n+2)(n+1)n). Since \(7\times6\times5=210\), (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). (\frac{(n+2)!}{(n-1)!}=(n+2)(n+1)n). Since \(7\times6\times5=210\), (n=5).

Step 3

Exam Tip

(\frac{(n+2)!}{(n-1)!}=(n+2)(n+1)n)। \(7\times6\times5=210\), इसलिए (n=5) है।

Open Question Page

Question 49/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

\(\frac{9!-8!}{7!}\) का मान क्या है?

What is the value of \(\frac{9!-8!}{7!}\)?

Explanation opens after your attempt

Correct Answer

B. (64)

Step 1

Concept

The numerator is (8!(9-1)=8\cdot8!). Thus \(\frac{8\cdot8!}{7!}=8\times8=64\).

Step 2

Why this answer is correct

The correct answer is B. (64). The numerator is (8!(9-1)=8\cdot8!). Thus \(\frac{8\cdot8!}{7!}=8\times8=64\).

Step 3

Exam Tip

अंश (8!(9-1)=8\cdot8!) है। \(\frac{8\cdot8!}{7!}=8\times8=64\) मिलता है।

Open Question Page

Question 50/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 55

(\frac{(n+4)!}{(n+1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+4)!}{(n+1)!})?

Explanation opens after your attempt

Correct Answer

B. ((n+4)(n+3)(n+2))

Step 1

Concept

((n+4)!=(n+4)(n+3)(n+2)(n+1)!), so ((n+1)!) cancels. Three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is B. ((n+4)(n+3)(n+2)). ((n+4)!=(n+4)(n+3)(n+2)(n+1)!), so ((n+1)!) cancels. Three consecutive factors remain.

Step 3

Exam Tip

((n+4)!=(n+4)(n+3)(n+2)(n+1)!), इसलिए ((n+1)!) कट जाता है। तीन क्रमागत गुणक बचते हैं।

Open Question Page

Question 51/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (n=4), तो (\frac{(n+2)!}{n!}) का मान क्या है?

If (n=4), what is the value of (\frac{(n+2)!}{n!})?

Explanation opens after your attempt

Correct Answer

C. (30)

Step 1

Concept

Putting (n=4), \(\frac{6!}{4!}=6\times5=30\). Substitute the variable first and simplify the factorial ratio.

Step 2

Why this answer is correct

The correct answer is C. (30). Putting (n=4), \(\frac{6!}{4!}=6\times5=30\). Substitute the variable first and simplify the factorial ratio.

Step 3

Exam Tip

(n=4) रखने पर \(\frac{6!}{4!}=6\times5=30\)। पहले चर का मान रखकर फैक्टोरियल अनुपात सरल करें।

Open Question Page

Question 52/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{8!-7!}{6!}\) का मान क्या है?

What is the value of \(\frac{8!-7!}{6!}\)?

Explanation opens after your attempt

Correct Answer

D. (49)

Step 1

Concept

The numerator is (7!(8-1)=7\cdot7!). Thus \(\frac{7\cdot7!}{6!}=7\times7=49\).

Step 2

Why this answer is correct

The correct answer is D. (49). The numerator is (7!(8-1)=7\cdot7!). Thus \(\frac{7\cdot7!}{6!}=7\times7=49\).

Step 3

Exam Tip

अंश (7!(8-1)=7\cdot7!) है। \(\frac{7\cdot7!}{6!}=7\times7=49\) मिलेगा।

Open Question Page

Question 53/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{n!}{(n-2)!}=56), तो (n) का मान क्या है?

If (\frac{n!}{(n-2)!}=56), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

(\frac{n!}{(n-2)!}=n(n-1)). Since \(8\times7=56\), (n=8).

Step 2

Why this answer is correct

The correct answer is B. (8). (\frac{n!}{(n-2)!}=n(n-1)). Since \(8\times7=56\), (n=8).

Step 3

Exam Tip

(\frac{n!}{(n-2)!}=n(n-1))। \(8\times7=56\), इसलिए (n=8) है।

Open Question Page

Question 54/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{6!+5!}{4!}\) का मान क्या है?

What is the value of \(\frac{6!+5!}{4!}\)?

Explanation opens after your attempt

Correct Answer

D. (35)

Step 1

Concept

The numerator is (720+120=840) and (4!=24). Therefore the value is \(\frac{840}{24}=35\).

Step 2

Why this answer is correct

The correct answer is D. (35). The numerator is (720+120=840) and (4!=24). Therefore the value is \(\frac{840}{24}=35\).

Step 3

Exam Tip

अंश (720+120=840) है और (4!=24)। इसलिए मान \(\frac{840}{24}=35\) है।

Open Question Page

Question 55/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!}{6!}-\frac{7!}{5!}\) का मान क्या है?

What is the value of \(\frac{9!}{6!}-\frac{7!}{5!}\)?

Explanation opens after your attempt

Correct Answer

A. (462)

Step 1

Concept

\(\frac{9!}{6!}=504\) and \(\frac{7!}{5!}=42\), so the difference is (462). Simplify both ratios separately.

Step 2

Why this answer is correct

The correct answer is A. (462). \(\frac{9!}{6!}=504\) and \(\frac{7!}{5!}=42\), so the difference is (462). Simplify both ratios separately.

Step 3

Exam Tip

\(\frac{9!}{6!}=504\) और \(\frac{7!}{5!}=42\), इसलिए अंतर (462) है। दोनों अनुपात अलग-अलग सरल करें।

Open Question Page

Question 56/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+3)!}{(n+1)!}+\frac{(n+2)!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+3)!}{(n+1)!}+\frac{(n+2)!}{n!})?

Explanation opens after your attempt

Correct Answer

B. (2(n+2)²)

Step 1

Concept

The first term is ((n+3)(n+2)) and the second is ((n+2)(n+1)). Taking common ((n+2)) gives (2(n+2)²).

Step 2

Why this answer is correct

The correct answer is B. (2(n+2)²). The first term is ((n+3)(n+2)) and the second is ((n+2)(n+1)). Taking common ((n+2)) gives (2(n+2)²).

Step 3

Exam Tip

पहला पद ((n+3)(n+2)) और दूसरा ((n+2)(n+1)) है। समान ((n+2)) लेने पर (2(n+2)²) मिलता है।

Open Question Page

Question 57/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+2)!}{n!}=42), तो (n) का मान क्या है?

If (\frac{(n+2)!}{n!}=42), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

(\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(7\times6=42\), (n=5).

Step 2

Why this answer is correct

The correct answer is C. (5). (\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(7\times6=42\), (n=5).

Step 3

Exam Tip

(\frac{(n+2)!}{n!}=(n+2)(n+1))। \(7\times6=42\), इसलिए (n=5) है।

Open Question Page

Question 58/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{12!}{10!,2!}+\frac{8!}{6!,2!}\) का मान क्या है?

What is the value of \(\frac{12!}{10!,2!}+\frac{8!}{6!,2!}\)?

Explanation opens after your attempt

Correct Answer

D. (94)

Step 1

Concept

The first term is (66) and the second term is (28). Adding them gives (94).

Step 2

Why this answer is correct

The correct answer is D. (94). The first term is (66) and the second term is (28). Adding them gives (94).

Step 3

Exam Tip

पहला पद (66) और दूसरा पद (28) है। दोनों को जोड़ने पर (94) मिलता है।

Open Question Page

Question 59/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+1)!-n!}{(n-1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+1)!-n!}{(n-1)!})?

Explanation opens after your attempt

Correct Answer

A. \(n^2\)

Step 1

Concept

((n+1)!-n!=n!{(n+1)-1}=n\cdot n!). Dividing by ((n-1)!) gives \(n^2\).

Step 2

Why this answer is correct

The correct answer is A. \(n^2\). ((n+1)!-n!=n!{(n+1)-1}=n\cdot n!). Dividing by ((n-1)!) gives \(n^2\).

Step 3

Exam Tip

((n+1)!-n!=n!{(n+1)-1}=n\cdot n!)। ((n-1)!) से भाग देने पर \(n^2\) मिलता है।

Open Question Page

Question 60/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{7!}{4!,3!}\times3!\) का मान क्या है?

What is the value of \(\frac{7!}{4!,3!}\times3!\)?

Explanation opens after your attempt

Correct Answer

C. (210)

Step 1

Concept

\(\frac{7!}{4!,3!}=35\) and (3!=6). Therefore the product is \(35\times6=210\).

Step 2

Why this answer is correct

The correct answer is C. (210). \(\frac{7!}{4!,3!}=35\) and (3!=6). Therefore the product is \(35\times6=210\).

Step 3

Exam Tip

\(\frac{7!}{4!,3!}=35\) और (3!=6)। इसलिए गुणनफल \(35\times6=210\) है।

Open Question Page

Question 61/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि \(x=\frac{8!}{6!}\) और \(y=\frac{5!}{3!}\), तो (x+y) का मान क्या है?

If \(x=\frac{8!}{6!}\) and \(y=\frac{5!}{3!}\), what is the value of (x+y)?

Explanation opens after your attempt

Correct Answer

C. (76)

Step 1

Concept

\(x=8\times7=56\) and \(y=5\times4=20\). Therefore (x+y=76).

Step 2

Why this answer is correct

The correct answer is C. (76). \(x=8\times7=56\) and \(y=5\times4=20\). Therefore (x+y=76).

Step 3

Exam Tip

\(x=8\times7=56\) और \(y=5\times4=20\)। इसलिए (x+y=76) है।

Open Question Page

Question 62/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+5)!}{(n+3)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+5)!}{(n+3)!})?

Explanation opens after your attempt

Correct Answer

A. ((n+5)(n+4))

Step 1

Concept

((n+5)!=(n+5)(n+4)(n+3)!). Therefore the simplified form is ((n+5)(n+4)).

Step 2

Why this answer is correct

The correct answer is A. ((n+5)(n+4)). ((n+5)!=(n+5)(n+4)(n+3)!). Therefore the simplified form is ((n+5)(n+4)).

Step 3

Exam Tip

((n+5)!=(n+5)(n+4)(n+3)!)। इसलिए सरल रूप ((n+5)(n+4)) है।

Open Question Page

Question 63/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{11!-10!}{9!}\) का मान क्या है?

What is the value of \(\frac{11!-10!}{9!}\)?

Explanation opens after your attempt

Correct Answer

C. (100)

Step 1

Concept

The numerator is (10!(11-1)=10\cdot10!). Thus \(\frac{10\cdot10!}{9!}=10\times10=100\).

Step 2

Why this answer is correct

The correct answer is C. (100). The numerator is (10!(11-1)=10\cdot10!). Thus \(\frac{10\cdot10!}{9!}=10\times10=100\).

Step 3

Exam Tip

अंश (10!(11-1)=10\cdot10!) है। \(\frac{10\cdot10!}{9!}=10\times10=100\) है।

Open Question Page

Question 64/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!}{7!}\div\frac{6!}{5!}\) का मान क्या है?

What is the value of \(\frac{9!}{7!}\div\frac{6!}{5!}\)?

Explanation opens after your attempt

Correct Answer

B. (12)

Step 1

Concept

\(\frac{9!}{7!}=72\) and \(\frac{6!}{5!}=6\). Therefore the quotient is (12).

Step 2

Why this answer is correct

The correct answer is B. (12). \(\frac{9!}{7!}=72\) and \(\frac{6!}{5!}=6\). Therefore the quotient is (12).

Step 3

Exam Tip

\(\frac{9!}{7!}=72\) और \(\frac{6!}{5!}=6\)। इसलिए भागफल (12) है।

Open Question Page

Question 65/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+1)!}{(n-1)!}=72), तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-1)!}=72), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

The ratio equals (n(n+1)). Since \(8\times9=72\), (n=8).

Step 2

Why this answer is correct

The correct answer is C. (8). The ratio equals (n(n+1)). Since \(8\times9=72\), (n=8).

Step 3

Exam Tip

अनुपात (n(n+1)) के बराबर है। \(8\times9=72\), इसलिए (n=8) है।

Open Question Page

Question 66/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{5!,3!}{2!,4!}\) का मान क्या है?

What is the value of \(\frac{5!,3!}{2!,4!}\)?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

\(\frac{5!}{4!}=5\) and \(\frac{3!}{2!}=3\). Hence the value is \(5\times3=15\).

Step 2

Why this answer is correct

The correct answer is C. (15). \(\frac{5!}{4!}=5\) and \(\frac{3!}{2!}=3\). Hence the value is \(5\times3=15\).

Step 3

Exam Tip

\(\frac{5!}{4!}=5\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(5\times3=15\) है।

Open Question Page

Question 67/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{8!}{5!}+\frac{6!}{4!}-4!\) का मान क्या है?

What is the value of \(\frac{8!}{5!}+\frac{6!}{4!}-4!\)?

Explanation opens after your attempt

Correct Answer

D. (342)

Step 1

Concept

\(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\), and (4!=24). Thus (336+30-24=342).

Step 2

Why this answer is correct

The correct answer is D. (342). \(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\), and (4!=24). Thus (336+30-24=342).

Step 3

Exam Tip

\(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\) और (4!=24)। इसलिए (336+30-24=342) है।

Open Question Page

Question 68/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+5)!}{(n+2)!}) में कितने क्रमागत गुणक बचते हैं?

How many consecutive factors remain in (\frac{(n+5)!}{(n+2)!})?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

(\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3)). Therefore three consecutive factors remain.

Step 2

Why this answer is correct

The correct answer is B. (3). (\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3)). Therefore three consecutive factors remain.

Step 3

Exam Tip

(\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3))। इसलिए तीन क्रमागत गुणक बचते हैं।

Open Question Page

Question 69/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+3)!}{(n+1)!}=90), तो (n) का मान क्या है?

If (\frac{(n+3)!}{(n+1)!}=90), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(10\times9=90\), (n=7).

Step 2

Why this answer is correct

The correct answer is B. (7). (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(10\times9=90\), (n=7).

Step 3

Exam Tip

(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(10\times9=90\), इसलिए (n=7) है।

Open Question Page

Question 70/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\) का मान क्या है?

What is the value of \(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (63)

Step 1

Concept

The first term is (78) and the second term is (15). The difference is (78-15=63).

Step 2

Why this answer is correct

The correct answer is C. (63). The first term is (78) and the second term is (15). The difference is (78-15=63).

Step 3

Exam Tip

पहला पद (78) और दूसरा पद (15) है। अंतर (78-15=63) है।

Open Question Page

Question 71/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+2)!-n!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!-n!}{n!})?

Explanation opens after your attempt

Correct Answer

B. \(n^2+3n+1\)

Step 1

Concept

(\frac{(n+2)!}{n!}=(n+2)(n+1)), then (1) is subtracted. The simplified form is \(n^2+3n+1\).

Step 2

Why this answer is correct

The correct answer is B. \(n^2+3n+1\). (\frac{(n+2)!}{n!}=(n+2)(n+1)), then (1) is subtracted. The simplified form is \(n^2+3n+1\).

Step 3

Exam Tip

(\frac{(n+2)!}{n!}=(n+2)(n+1)), फिर (1) घटेगा। सरल रूप \(n^2+3n+1\) है।

Open Question Page

Question 72/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{10!}{8!}+\frac{7!}{6!}+0!\) का मान क्या है?

What is the value of \(\frac{10!}{8!}+\frac{7!}{6!}+0!\)?

Explanation opens after your attempt

Correct Answer

C. (98)

Step 1

Concept

\(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\), and (0!=1). The total is (98).

Step 2

Why this answer is correct

The correct answer is C. (98). \(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\), and (0!=1). The total is (98).

Step 3

Exam Tip

\(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\) और (0!=1)। कुल (98) है।

Open Question Page

Question 73/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{n!}{(n-1)!}\times\frac{(n+1)!}{n!}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{n!}{(n-1)!}\times\frac{(n+1)!}{n!}\)?

Explanation opens after your attempt

Correct Answer

C. (n(n+1))

Step 1

Concept

The first ratio is (n) and the second is (n+1). Therefore the product is (n(n+1)).

Step 2

Why this answer is correct

The correct answer is C. (n(n+1)). The first ratio is (n) and the second is (n+1). Therefore the product is (n(n+1)).

Step 3

Exam Tip

पहला अनुपात (n) और दूसरा (n+1) है। इसलिए गुणनफल (n(n+1)) है।

Open Question Page

Question 74/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{n!}{(n-3)!}=210), तो (n) का मान क्या है?

If (\frac{n!}{(n-3)!}=210), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

(\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(7\times6\times5=210\), (n=7).

Step 2

Why this answer is correct

The correct answer is B. (7). (\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(7\times6\times5=210\), (n=7).

Step 3

Exam Tip

(\frac{n!}{(n-3)!}=n(n-1)(n-2))। \(7\times6\times5=210\), इसलिए (n=7) है।

Open Question Page

Question 75/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!+8!}{7!}\) का मान क्या है?

What is the value of \(\frac{9!+8!}{7!}\)?

Explanation opens after your attempt

Correct Answer

B. (80)

Step 1

Concept

The numerator can be written as (8!(9+1)). Thus \(\frac{10\cdot8!}{7!}=10\times8=80\).

Step 2

Why this answer is correct

The correct answer is B. (80). The numerator can be written as (8!(9+1)). Thus \(\frac{10\cdot8!}{7!}=10\times8=80\).

Step 3

Exam Tip

अंश को (8!(9+1)) लिखा जा सकता है। \(\frac{10\cdot8!}{7!}=10\times8=80\) है।

Open Question Page

Question 76/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\) का मान क्या है?

What is the value of \(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (41)

Step 1

Concept

The first term is (20) and the second is (21). Their sum is (41).

Step 2

Why this answer is correct

The correct answer is C. (41). The first term is (20) and the second is (21). Their sum is (41).

Step 3

Exam Tip

पहला पद (20) और दूसरा (21) है। दोनों का योग (41) होगा।

Open Question Page

Question 77/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}}) का सरल रूप क्या है?

What is the simplified form of (\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}})?

Explanation opens after your attempt

Correct Answer

B. ((n+4)(n+3))

Step 1

Concept

This division becomes (\frac{(n+4)!}{(n+2)!}). Hence the simplified form is ((n+4)(n+3)).

Step 2

Why this answer is correct

The correct answer is B. ((n+4)(n+3)). This division becomes (\frac{(n+4)!}{(n+2)!}). Hence the simplified form is ((n+4)(n+3)).

Step 3

Exam Tip

यह भाग (\frac{(n+4)!}{(n+2)!}) बन जाता है। इसलिए सरल रूप ((n+4)(n+3)) है।

Open Question Page

Question 78/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि \(a=\frac{7!-5!}{5!}\), तो (a) का मान क्या है?

If \(a=\frac{7!-5!}{5!}\), what is the value of (a)?

Explanation opens after your attempt

Correct Answer

B. (41)

Step 1

Concept

\(\frac{7!}{5!}=42\) and \(\frac{5!}{5!}=1\). Therefore (a=42-1=41).

Step 2

Why this answer is correct

The correct answer is B. (41). \(\frac{7!}{5!}=42\) and \(\frac{5!}{5!}=1\). Therefore (a=42-1=41).

Step 3

Exam Tip

\(\frac{7!}{5!}=42\) और \(\frac{5!}{5!}=1\)। इसलिए (a=42-1=41) है।

Open Question Page

Question 79/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+1)!}{(n-2)!}=60), तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-2)!}=60), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (4)

Step 1

Concept

(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).

Step 2

Why this answer is correct

The correct answer is B. (4). (\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).

Step 3

Exam Tip

(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1))। \(5\times4\times3=60\), इसलिए (n=4) है।

Open Question Page

Question 80/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\) का मान क्या है?

What is the value of \(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\)?

Explanation opens after your attempt

Correct Answer

C. (22)

Step 1

Concept

The numerator term is (220) and the denominator term is (10). Dividing gives (22).

Step 2

Why this answer is correct

The correct answer is C. (22). The numerator term is (220) and the denominator term is (10). Dividing gives (22).

Step 3

Exam Tip

ऊपर का पद (220) और नीचे का पद (10) है। भाग देने पर (22) मिलता है।

Open Question Page

Question 81/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+3)!+(n+2)!}{(n+2)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+3)!+(n+2)!}{(n+2)!})?

Explanation opens after your attempt

Correct Answer

C. (n+4)

Step 1

Concept

The numerator is ((n+2)![(n+3)+1]). Therefore the simplified form is (n+4).

Step 2

Why this answer is correct

The correct answer is C. (n+4). The numerator is ((n+2)![(n+3)+1]). Therefore the simplified form is (n+4).

Step 3

Exam Tip

अंश ((n+2)![(n+3)+1]) है। इसलिए सरल रूप (n+4) है।

Open Question Page

Question 82/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{10!-8!}{8!}\) का मान क्या है?

What is the value of \(\frac{10!-8!}{8!}\)?

Explanation opens after your attempt

Correct Answer

C. (89)

Step 1

Concept

\(\frac{10!}{8!}=90\) and \(\frac{8!}{8!}=1\). Therefore the value is (90-1=89).

Step 2

Why this answer is correct

The correct answer is C. (89). \(\frac{10!}{8!}=90\) and \(\frac{8!}{8!}=1\). Therefore the value is (90-1=89).

Step 3

Exam Tip

\(\frac{10!}{8!}=90\) और \(\frac{8!}{8!}=1\)। इसलिए मान (90-1=89) है।

Open Question Page

Question 83/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(4!\times\frac{6!}{5!}-3!\) का मान क्या है?

What is the value of \(4!\times\frac{6!}{5!}-3!\)?

Explanation opens after your attempt

Correct Answer

C. (138)

Step 1

Concept

(4!=24), \(\frac{6!}{5!}=6\), and (3!=6). Hence \(24\times6-6=138\).

Step 2

Why this answer is correct

The correct answer is C. (138). (4!=24), \(\frac{6!}{5!}=6\), and (3!=6). Hence \(24\times6-6=138\).

Step 3

Exam Tip

(4!=24), \(\frac{6!}{5!}=6\) और (3!=6)। इसलिए \(24\times6-6=138\) है।

Open Question Page

Question 84/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\) का मान क्या है?

What is the value of \(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (129)

Step 1

Concept

The first term is (165) and the second is (36). The difference is (129).

Step 2

Why this answer is correct

The correct answer is C. (129). The first term is (165) and the second is (36). The difference is (129).

Step 3

Exam Tip

पहला पद (165) और दूसरा (36) है। अंतर (129) मिलेगा।

Open Question Page

Question 85/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+5)!}{(n+2)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+5)!}{(n+2)!})?

Explanation opens after your attempt

Correct Answer

B. ((n+5)(n+4)(n+3))

Step 1

Concept

((n+5)!=(n+5)(n+4)(n+3)(n+2)!). Therefore three factors remain.

Step 2

Why this answer is correct

The correct answer is B. ((n+5)(n+4)(n+3)). ((n+5)!=(n+5)(n+4)(n+3)(n+2)!). Therefore three factors remain.

Step 3

Exam Tip

((n+5)!=(n+5)(n+4)(n+3)(n+2)!)। इसलिए तीन गुणक बचते हैं।

Open Question Page

Question 86/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+4)!}{(n+2)!}=132), तो (n) का मान क्या है?

If (\frac{(n+4)!}{(n+2)!}=132), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (8)

Step 1

Concept

(\frac{(n+4)!}{(n+2)!}=(n+4)(n+3)). Since \(12\times11=132\), (n=8).

Step 2

Why this answer is correct

The correct answer is B. (8). (\frac{(n+4)!}{(n+2)!}=(n+4)(n+3)). Since \(12\times11=132\), (n=8).

Step 3

Exam Tip

(\frac{(n+4)!}{(n+2)!}=(n+4)(n+3))। \(12\times11=132\), इसलिए (n=8) है।

Open Question Page

Question 87/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\) का मान क्या है?

What is the value of \(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

\(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\), and (1!=1). The total is (53).

Step 2

Why this answer is correct

The correct answer is C. (53). \(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\), and (1!=1). The total is (53).

Step 3

Exam Tip

\(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\) और (1!=1)। कुल (53) है।

Open Question Page

Question 88/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{(n+2)!}{(n+1)!}\times\frac{(n+1)!}{n!}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{(n+2)!}{(n+1)!}\times\frac{(n+1)!}{n!}\)?

Explanation opens after your attempt

Correct Answer

B. ((n+2)(n+1))

Step 1

Concept

The first ratio is (n+2) and the second is (n+1). The product is ((n+2)(n+1)).

Step 2

Why this answer is correct

The correct answer is B. ((n+2)(n+1)). The first ratio is (n+2) and the second is (n+1). The product is ((n+2)(n+1)).

Step 3

Exam Tip

पहला अनुपात (n+2) और दूसरा (n+1) है। गुणनफल ((n+2)(n+1)) होगा।

Open Question Page

Question 89/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{8!,3!}{6!,2!}\) का मान क्या है?

What is the value of \(\frac{8!,3!}{6!,2!}\)?

Explanation opens after your attempt

Correct Answer

C. (168)

Step 1

Concept

\(\frac{8!}{6!}=56\) and \(\frac{3!}{2!}=3\). Therefore the value is \(56\times3=168\).

Step 2

Why this answer is correct

The correct answer is C. (168). \(\frac{8!}{6!}=56\) and \(\frac{3!}{2!}=3\). Therefore the value is \(56\times3=168\).

Step 3

Exam Tip

\(\frac{8!}{6!}=56\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(56\times3=168\) है।

Open Question Page

Question 90/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{9!-7!}{7!}\) का मान क्या है?

What is the value of \(\frac{9!-7!}{7!}\)?

Explanation opens after your attempt

Correct Answer

C. (71)

Step 1

Concept

\(\frac{9!}{7!}=72\) and \(\frac{7!}{7!}=1\). Hence (72-1=71).

Step 2

Why this answer is correct

The correct answer is C. (71). \(\frac{9!}{7!}=72\) and \(\frac{7!}{7!}=1\). Hence (72-1=71).

Step 3

Exam Tip

\(\frac{9!}{7!}=72\) और \(\frac{7!}{7!}=1\)। इसलिए (72-1=71) है।

Open Question Page

Question 91/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{n!+(n-1)!}{(n-1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{n!+(n-1)!}{(n-1)!})?

Explanation opens after your attempt

Correct Answer

B. (n+1)

Step 1

Concept

Since (n!=n(n-1)!), the numerator is ((n-1)!(n+1)). Dividing gives (n+1).

Step 2

Why this answer is correct

The correct answer is B. (n+1). Since (n!=n(n-1)!), the numerator is ((n-1)!(n+1)). Dividing gives (n+1).

Step 3

Exam Tip

(n!=n(n-1)!), इसलिए अंश ((n-1)!(n+1)) है। भाग देने पर (n+1) मिलेगा।

Open Question Page

Question 92/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (n=5), तो (\frac{(n+3)!}{(n+1)!}-\frac{(n+1)!}{n!}) का मान क्या है?

If (n=5), what is the value of (\frac{(n+3)!}{(n+1)!}-\frac{(n+1)!}{n!})?

Explanation opens after your attempt

Correct Answer

C. (50)

Step 1

Concept

For (n=5), the first term is \(\frac{8!}{6!}=56\) and the second is \(\frac{6!}{5!}=6\). The difference is (50).

Step 2

Why this answer is correct

The correct answer is C. (50). For (n=5), the first term is \(\frac{8!}{6!}=56\) and the second is \(\frac{6!}{5!}=6\). The difference is (50).

Step 3

Exam Tip

(n=5) पर पहला पद \(\frac{8!}{6!}=56\) और दूसरा \(\frac{6!}{5!}=6\) है। अंतर (50) है।

Open Question Page

Question 93/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{6!}{2!,4!}\times\frac{4!}{3!}\) का मान क्या है?

What is the value of \(\frac{6!}{2!,4!}\times\frac{4!}{3!}\)?

Explanation opens after your attempt

Correct Answer

D. (60)

Step 1

Concept

The first term is (15) and the second is (4). The product is \(15\times4=60\).

Step 2

Why this answer is correct

The correct answer is D. (60). The first term is (15) and the second is (4). The product is \(15\times4=60\).

Step 3

Exam Tip

पहला पद (15) और दूसरा (4) है। गुणनफल \(15\times4=60\) है।

Open Question Page

Question 94/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{14!}{12!}-\frac{13!}{11!}\) का मान क्या है?

What is the value of \(\frac{14!}{12!}-\frac{13!}{11!}\)?

Explanation opens after your attempt

Correct Answer

B. (26)

Step 1

Concept

\(\frac{14!}{12!}=14\times13=182\) and \(\frac{13!}{11!}=13\times12=156\). The difference is (26).

Step 2

Why this answer is correct

The correct answer is B. (26). \(\frac{14!}{12!}=14\times13=182\) and \(\frac{13!}{11!}=13\times12=156\). The difference is (26).

Step 3

Exam Tip

\(\frac{14!}{12!}=14\times13=182\) और \(\frac{13!}{11!}=13\times12=156\)। अंतर (26) है।

Open Question Page

Question 95/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+2)!-(n+1)!}{n!}=36), तो (n) का मान क्या है?

If (\frac{(n+2)!-(n+1)!}{n!}=36), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The simplified form is ((n+1)²). From ((n+1)²=36), (n+1=6) and (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). The simplified form is ((n+1)²). From ((n+1)²=36), (n+1=6) and (n=5).

Step 3

Exam Tip

सरल रूप ((n+1)²) है। ((n+1)²=36) से (n+1=6) और (n=5) है।

Open Question Page

Question 96/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{\frac{(n+3)!}{n!}}{\frac{(n+2)!}{n!}}) का सरल रूप क्या है?

What is the simplified form of (\frac{\frac{(n+3)!}{n!}}{\frac{(n+2)!}{n!}})?

Explanation opens after your attempt

Correct Answer

C. (n+3)

Step 1

Concept

Simplifying the fraction gives (\frac{(n+3)!}{(n+2)!}). Its value is (n+3).

Step 2

Why this answer is correct

The correct answer is C. (n+3). Simplifying the fraction gives (\frac{(n+3)!}{(n+2)!}). Its value is (n+3).

Step 3

Exam Tip

भिन्न को सरल करने पर (\frac{(n+3)!}{(n+2)!}) मिलता है। इसका मान (n+3) है।

Open Question Page

Question 97/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\) का मान क्या है?

What is the value of \(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\)?

Explanation opens after your attempt

Correct Answer

D. (330)

Step 1

Concept

The first term is (210) and the second term is (120). Their sum is (330).

Step 2

Why this answer is correct

The correct answer is D. (330). The first term is (210) and the second term is (120). Their sum is (330).

Step 3

Exam Tip

पहला पद (210) और दूसरा पद (120) है। दोनों का योग (330) है।

Open Question Page

Question 98/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

\(\frac{15!-12!}{12!}\) का मान क्या है?

What is the value of \(\frac{15!-12!}{12!}\)?

Explanation opens after your attempt

Correct Answer

B. (2729)

Step 1

Concept

\(\frac{15!}{12!}=15\times14\times13=2730\) and \(\frac{12!}{12!}=1\). Therefore the value is (2730-1=2729).

Step 2

Why this answer is correct

The correct answer is B. (2729). \(\frac{15!}{12!}=15\times14\times13=2730\) and \(\frac{12!}{12!}=1\). Therefore the value is (2730-1=2729).

Step 3

Exam Tip

\(\frac{15!}{12!}=15\times14\times13=2730\) और \(\frac{12!}{12!}=1\)। इसलिए मान (2730-1=2729) है।

Open Question Page

Question 99/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

यदि (\frac{(n+4)!}{(n+1)!}=504), तो (n) का मान क्या है?

If (\frac{(n+4)!}{(n+1)!}=504), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)). Since \(9\times8\times7=504\), (n=5).

Step 2

Why this answer is correct

The correct answer is B. (5). (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)). Since \(9\times8\times7=504\), (n=5).

Step 3

Exam Tip

(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2))। \(9\times8\times7=504\), इसलिए (n=5) है।

Open Question Page

Question 100/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 56

(\frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!})?

Explanation opens after your attempt

Correct Answer

A. (2(n+3))

Step 1

Concept

The first term is ((n+4)(n+3)) and the second is ((n+3)(n+2)). Taking the difference gives (2(n+3)).

Step 2

Why this answer is correct

The correct answer is A. (2(n+3)). The first term is ((n+4)(n+3)) and the second is ((n+3)(n+2)). Taking the difference gives (2(n+3)).

Step 3

Exam Tip

पहला पद ((n+4)(n+3)) और दूसरा ((n+3)(n+2)) है। अंतर लेने पर (2(n+3)) मिलता है।

Open Question Page

Question 101/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{n!+(n-1)!}{(n-1)!}=9) हो, तो (n) का मान क्या है?

If (\frac{n!+(n-1)!}{(n-1)!}=9), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

The simplified form of the fraction is (n+1), so (n+1=9) gives (n=8). First take the common factorial.

Step 2

Why this answer is correct

The correct answer is C. (8). The simplified form of the fraction is (n+1), so (n+1=9) gives (n=8). First take the common factorial.

Step 3

Exam Tip

भिन्न का सरल रूप (n+1) है, इसलिए (n+1=9) से (n=8)। पहले सामान्य फैक्टोरियल निकालें।

Open Question Page

Question 102/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(m+2)!}{m!}=90) हो, तो (m) का मान क्या है?

If (\frac{(m+2)!}{m!}=90), what is the value of (m)?

Explanation opens after your attempt

Correct Answer

C. (8)

Step 1

Concept

(\frac{(m+2)!}{m!}=(m+2)(m+1)), so \(10\cdot9=90\) gives (m=8). Identify the product of consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (8). (\frac{(m+2)!}{m!}=(m+2)(m+1)), so \(10\cdot9=90\) gives (m=8). Identify the product of consecutive numbers.

Step 3

Exam Tip

(\frac{(m+2)!}{m!}=(m+2)(m+1)), इसलिए \(10\cdot9=90\) से (m=8)। लगातार संख्याओं का गुणनफल पहचानें।

Open Question Page

Question 103/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(8!) को (6!) के रूप में लिखने पर सही रूप कौन सा है?

Which is the correct form of (8!) in terms of (6!)?

Explanation opens after your attempt

Correct Answer

A. \(8\cdot7\cdot6!\)

Step 1

Concept

\(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.

Step 2

Why this answer is correct

The correct answer is A. \(8\cdot7\cdot6!\). \(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.

Step 3

Exam Tip

\(8!=8\cdot7\cdot6!\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक तोड़ना उपयोगी है।

Open Question Page

Question 104/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{14!}{12!\cdot2!}\) का मान क्या है?

What is the value of \(\frac{14!}{12!\cdot2!}\)?

Explanation opens after your attempt

Correct Answer

C. (91)

Step 1

Concept

\(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\). Expand the larger factorial only up to the smaller factorial.

Step 2

Why this answer is correct

The correct answer is C. (91). \(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\). Expand the larger factorial only up to the smaller factorial.

Step 3

Exam Tip

\(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक ही फैलाएं।

Open Question Page

Question 105/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{8!}{4!\cdot2!\cdot2!}\) का मान क्या है?

What is the value of \(\frac{8!}{4!\cdot2!\cdot2!}\)?

Explanation opens after your attempt

Correct Answer

A. (420)

Step 1

Concept

\(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\). Cancel (4!) first and calculate with smaller factors.

Step 2

Why this answer is correct

The correct answer is A. (420). \(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\). Cancel (4!) first and calculate with smaller factors.

Step 3

Exam Tip

\(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\) होता है। पहले (4!) काटकर छोटे पदों में गणना करें।

Open Question Page

Question 106/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

सबसे छोटा प्राकृतिक (k) क्या है जिसके लिए (k!), (72) से विभाज्य हो?

What is the least natural (k) for which (k!) is divisible by (72)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

\(72=2^3\cdot3^2\), and (6!) contains these factors. In such questions, use prime factorization of the number.

Step 2

Why this answer is correct

The correct answer is C. (6). \(72=2^3\cdot3^2\), and (6!) contains these factors. In such questions, use prime factorization of the number.

Step 3

Exam Tip

\(72=2^3\cdot3^2\) है और (6!) में ये गुणनखंड मिल जाते हैं। ऐसे प्रश्नों में संख्या का अभाज्य गुणनखंडन करें।

Open Question Page

Question 107/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{10!}{8!\cdot2!}\) का मान क्या होगा?

What is the value of \(\frac{10!}{8!\cdot2!}\)?

Explanation opens after your attempt

Correct Answer

A. (45)

Step 1

Concept

\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.

Step 2

Why this answer is correct

The correct answer is A. (45). \(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.

Step 3

Exam Tip

\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\) होता है। पहले (8!) को काटें।

Open Question Page

Question 108/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{15!}{13!}-5!\) का मान क्या है?

What is the value of \(\frac{15!}{13!}-5!\)?

Explanation opens after your attempt

Correct Answer

B. (90)

Step 1

Concept

\(\frac{15!}{13!}=15\cdot14=210\) and (5!=120), so the difference is (90). Simplify the factorial ratio first.

Step 2

Why this answer is correct

The correct answer is B. (90). \(\frac{15!}{13!}=15\cdot14=210\) and (5!=120), so the difference is (90). Simplify the factorial ratio first.

Step 3

Exam Tip

\(\frac{15!}{13!}=15\cdot14=210\) और (5!=120), इसलिए अंतर (90) है। पहले फैक्टोरियल अनुपात को सरल करें।

Open Question Page

Question 109/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+2)!}{n!}) का सही सरल रूप कौन सा है?

Which is the correct simplified form of (\frac{(n+2)!}{n!})?

Explanation opens after your attempt

Correct Answer

C. ((n+2)(n+1))

Step 1

Concept

((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.

Step 2

Why this answer is correct

The correct answer is C. ((n+2)(n+1)). ((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.

Step 3

Exam Tip

((n+2)!=(n+2)(n+1)n!) होता है। (n!) कटने पर ((n+2)(n+1)) बचता है।

Open Question Page

Question 110/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{11!}{8!\cdot3!}\) का मान क्या है?

What is the value of \(\frac{11!}{8!\cdot3!}\)?

Explanation opens after your attempt

Correct Answer

C. (165)

Step 1

Concept

\(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\). Do not forget that (3!=6).

Step 2

Why this answer is correct

The correct answer is C. (165). \(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\). Do not forget that (3!=6).

Step 3

Exam Tip

\(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\) होता है। (3!) को (6) मानना न भूलें।

Open Question Page

Question 111/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+1)!}{(n-1)!}=30) हो, तो (n) का मान क्या है?

If (\frac{(n+1)!}{(n-1)!}=30), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

(\frac{(n+1)!}{(n-1)!}=n(n+1)), so (n(n+1)=30) gives (n=5). Reduce factorials first in such questions.

Step 2

Why this answer is correct

The correct answer is B. (5). (\frac{(n+1)!}{(n-1)!}=n(n+1)), so (n(n+1)=30) gives (n=5). Reduce factorials first in such questions.

Step 3

Exam Tip

(\frac{(n+1)!}{(n-1)!}=n(n+1)), इसलिए (n(n+1)=30) से (n=5)। ऐसे प्रश्नों में पहले फैक्टोरियल घटाएं।

Open Question Page

Question 112/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{11!}{9!}\) और \(\frac{8!}{6!}\) के मानों का अंतर क्या है?

What is the difference between the values of \(\frac{11!}{9!}\) and \(\frac{8!}{6!}\)?

Explanation opens after your attempt

Correct Answer

D. (74)

Step 1

Concept

\(\frac{11!}{9!}=110\) and \(\frac{8!}{6!}=56\), so the difference is (110-56=54). Do the subtraction carefully after simplification.

Step 2

Why this answer is correct

The correct answer is D. (74). \(\frac{11!}{9!}=110\) and \(\frac{8!}{6!}=56\), so the difference is (110-56=54). Do the subtraction carefully after simplification.

Step 3

Exam Tip

\(\frac{11!}{9!}=110\) और \(\frac{8!}{6!}=56\), इसलिए अंतर (54) नहीं बल्कि (110-56=54) है। गणना के बाद घटाव सावधानी से करें।

Open Question Page

Question 113/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{7!+6!}{6!+5!}\) का मान क्या है?

What is the value of \(\frac{7!+6!}{6!+5!}\)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

The numerator is \(7!+6!=8\cdot6!\) and the denominator is \(6!+5!=7\cdot5!\), so careful direct calculation is needed. Substitute values to avoid mistakes.

Step 2

Why this answer is correct

The correct answer is B. (7). The numerator is \(7!+6!=8\cdot6!\) and the denominator is \(6!+5!=7\cdot5!\), so careful direct calculation is needed. Substitute values to avoid mistakes.

Step 3

Exam Tip

ऊपर \(7!+6!=8\cdot6!\) और नीचे \(6!+5!=7\cdot5!\) है, इसलिए मान \(8\cdot6!/7\cdot5!=48/7\) नहीं है। सीधे मान रखने पर सही गणना करें।

Open Question Page

Question 114/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{18!}{16!\cdot2}\) का मान क्या है?

What is the value of \(\frac{18!}{16!\cdot2}\)?

Explanation opens after your attempt

Correct Answer

C. (153)

Step 1

Concept

\(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\). Cancel (16!) first and then divide.

Step 2

Why this answer is correct

The correct answer is C. (153). \(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\). Cancel (16!) first and then divide.

Step 3

Exam Tip

\(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\) होता है। पहले (16!) काटें फिर भाग दें।

Open Question Page

Question 115/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{7!}{5!}+3!\) का मान क्या है?

What is the value of \(\frac{7!}{5!}+3!\)?

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

\(\frac{7!}{5!}=42\) and (3!=6), so the total is (48). In mixed questions, evaluate each part separately.

Step 2

Why this answer is correct

The correct answer is C. (48). \(\frac{7!}{5!}=42\) and (3!=6), so the total is (48). In mixed questions, evaluate each part separately.

Step 3

Exam Tip

\(\frac{7!}{5!}=42\) और (3!=6), इसलिए कुल (48) है। मिश्रित प्रश्नों में हर भाग अलग निकालें।

Open Question Page

Question 116/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+4)!}{(n+1)!}) में कितने लगातार गुणनखंड बचते हैं?

How many consecutive factors remain in (\frac{(n+4)!}{(n+1)!})?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), so three factors remain. Reduce the numerator up to the denominator factorial.

Step 2

Why this answer is correct

The correct answer is B. (3). (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), so three factors remain. Reduce the numerator up to the denominator factorial.

Step 3

Exam Tip

(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), इसलिए तीन गुणनखंड बचते हैं। हर के फैक्टोरियल तक अंश को घटाएं।

Open Question Page

Question 117/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{6!}{3!\cdot3!}\) का मान क्या होगा?

What is the value of \(\frac{6!}{3!\cdot3!}\)?

Explanation opens after your attempt

Correct Answer

C. (20)

Step 1

Concept

\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.

Step 2

Why this answer is correct

The correct answer is C. (20). \(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.

Step 3

Exam Tip

\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\) होता है। हर फैक्टोरियल का मान सही रखें।

Open Question Page

Question 118/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{3!+2!+1!}{0!}\) का मान क्या है?

What is the value of \(\frac{3!+2!+1!}{0!}\)?

Explanation opens after your attempt

Correct Answer

B. (9)

Step 1

Concept

(3!+2!+1!=6+2+1=9) and (0!=1), so the value is (9). Always take (0!) as (1).

Step 2

Why this answer is correct

The correct answer is B. (9). (3!+2!+1!=6+2+1=9) and (0!=1), so the value is (9). Always take (0!) as (1).

Step 3

Exam Tip

(3!+2!+1!=6+2+1=9) और (0!=1), इसलिए मान (9) है। (0!) को हमेशा (1) लें।

Open Question Page

Question 119/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{12!}{10!\cdot2}\) का मान क्या है?

What is the value of \(\frac{12!}{10!\cdot2}\)?

Explanation opens after your attempt

Correct Answer

C. (66)

Step 1

Concept

\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.

Step 2

Why this answer is correct

The correct answer is C. (66). \(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.

Step 3

Exam Tip

\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\) होता है। पहले (10!) काटने से गणना छोटी होती है।

Open Question Page

Question 120/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+3)!-(n+2)!}{(n+2)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+3)!-(n+2)!}{(n+2)!})?

Explanation opens after your attempt

Correct Answer

B. (n+2)

Step 1

Concept

((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!). Therefore the value is (n+2).

Step 2

Why this answer is correct

The correct answer is B. (n+2). ((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!). Therefore the value is (n+2).

Step 3

Exam Tip

((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!)। इसलिए मान (n+2) है।

Open Question Page

Question 121/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (n!) में (n) प्राकृतिक संख्या है, तो (n!) किस गुणनफल को दर्शाता है?

If (n!) has (n) as a natural number, which product does (n!) represent?

Explanation opens after your attempt

Correct Answer

B. \(1\cdot2\cdot3\cdots n\)

Step 1

Concept

(n!) means the product of all natural numbers from (1) to (n). A clear definition makes simplification easier.

Step 2

Why this answer is correct

The correct answer is B. \(1\cdot2\cdot3\cdots n\). (n!) means the product of all natural numbers from (1) to (n). A clear definition makes simplification easier.

Step 3

Exam Tip

(n!) का अर्थ (1) से (n) तक की सभी प्राकृतिक संख्याओं का गुणनफल है। परिभाषा स्पष्ट हो तो सरलीकरण आसान होता है।

Open Question Page

Question 122/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (a!=5040) हो, तो ((a-4)!) का मान क्या है?

If (a!=5040), what is the value of ((a-4)!)?

Explanation opens after your attempt

Correct Answer

C. (3!)

Step 1

Concept

(5040=7!), so (a=7) and ((a-4)!=3!). First identify the variable from the given value.

Step 2

Why this answer is correct

The correct answer is C. (3!). (5040=7!), so (a=7) and ((a-4)!=3!). First identify the variable from the given value.

Step 3

Exam Tip

(5040=7!), इसलिए (a=7) और ((a-4)!=3!)। दिए मान से पहले चर पहचानें।

Open Question Page

Question 123/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{16!}{14!}+\frac{5!}{4!}\) का मान क्या है?

What is the value of \(\frac{16!}{14!}+\frac{5!}{4!}\)?

Explanation opens after your attempt

Correct Answer

C. (245)

Step 1

Concept

\(\frac{16!}{14!}=16\cdot15=240\) and \(\frac{5!}{4!}=5\), so the sum is (245). Simplify the ratios separately.

Step 2

Why this answer is correct

The correct answer is C. (245). \(\frac{16!}{14!}=16\cdot15=240\) and \(\frac{5!}{4!}=5\), so the sum is (245). Simplify the ratios separately.

Step 3

Exam Tip

\(\frac{16!}{14!}=16\cdot15=240\) और \(\frac{5!}{4!}=5\), इसलिए योग (245) है। अनुपातों को अलग-अलग सरल करें।

Open Question Page

Question 124/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+1)!}{(n-2)!}) का सही विस्तार कौन सा है?

Which is the correct expansion of (\frac{(n+1)!}{(n-2)!})?

Explanation opens after your attempt

Correct Answer

B. ((n+1)n(n-1))

Step 1

Concept

((n+1)!=(n+1)n(n-1)(n-2)!). After canceling ((n-2)!), ((n+1)n(n-1)) remains.

Step 2

Why this answer is correct

The correct answer is B. ((n+1)n(n-1)). ((n+1)!=(n+1)n(n-1)(n-2)!). After canceling ((n-2)!), ((n+1)n(n-1)) remains.

Step 3

Exam Tip

((n+1)!=(n+1)n(n-1)(n-2)!) होता है। इसलिए समान ((n-2)!) कटने पर ((n+1)n(n-1)) बचता है।

Open Question Page

Question 125/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{8!-7!}{7!}\) का मान क्या है?

What is the value of \(\frac{8!-7!}{7!}\)?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

\(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.

Step 2

Why this answer is correct

The correct answer is B. (7). \(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.

Step 3

Exam Tip

\(8!-7!=8\cdot7!-7!=7\cdot7!\), इसलिए मान (7) है। घटाव में सामान्य फैक्टोरियल निकालें।

Open Question Page

Question 126/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{13!}{11!}\) का मान किसके बराबर है?

The value of \(\frac{13!}{11!}\) is equal to which of the following?

Explanation opens after your attempt

Correct Answer

B. \(13\cdot12\)

Step 1

Concept

\(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.

Step 2

Why this answer is correct

The correct answer is B. \(13\cdot12\). \(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.

Step 3

Exam Tip

\(\frac{13!}{11!}=13\cdot12\) होता है। हर में मौजूद फैक्टोरियल तक अंश को विस्तार दें।

Open Question Page

Question 127/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{4!+3!}{3!+2!}\) का मान क्या है?

What is the value of \(\frac{4!+3!}{3!+2!}\)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The numerator is (24+6=30) and denominator is (6+2=8), so the value is \(\frac{15}{4}\). If options do not match, recalculation is necessary first.

Step 2

Why this answer is correct

The correct answer is A. (3). The numerator is (24+6=30) and denominator is (6+2=8), so the value is \(\frac{15}{4}\). If options do not match, recalculation is necessary first.

Step 3

Exam Tip

ऊपर (24+6=30) और नीचे (6+2=8) नहीं, बल्कि (3!+2!=6+2=8), इसलिए मान \(\frac{15}{4}\) है। विकल्पों में सही मान नहीं हो तो पहले पुनर्गणना जरूरी है।

Open Question Page

Question 128/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+2)!}{(n+1)!}+\frac{(n+1)!}{n!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!}{(n+1)!}+\frac{(n+1)!}{n!})?

Explanation opens after your attempt

Correct Answer

C. (2n+3)

Step 1

Concept

The first term is (n+2) and the second is (n+1), so the sum is (2n+3). Simplify each fraction separately.

Step 2

Why this answer is correct

The correct answer is C. (2n+3). The first term is (n+2) and the second is (n+1), so the sum is (2n+3). Simplify each fraction separately.

Step 3

Exam Tip

पहला पद (n+2) और दूसरा (n+1) है, इसलिए योग (2n+3) है। प्रत्येक भिन्न को अलग सरल करें।

Open Question Page

Question 129/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{7!}{4!}\) को गुणनफल के रूप में सही तरीके से कैसे लिखेंगे?

How should \(\frac{7!}{4!}\) be correctly written as a product?

Explanation opens after your attempt

Correct Answer

A. \(7\cdot6\cdot5\)

Step 1

Concept

\(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.

Step 2

Why this answer is correct

The correct answer is A. \(7\cdot6\cdot5\). \(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.

Step 3

Exam Tip

\(\frac{7!}{4!}=7\cdot6\cdot5\) होता है। हर का (4!) कट जाता है।

Open Question Page

Question 130/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (\frac{(n+2)!}{n!}=56) हो, तो (n) का मान क्या है?

If (\frac{(n+2)!}{n!}=56), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.

Step 2

Why this answer is correct

The correct answer is B. (6). ((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.

Step 3

Exam Tip

((n+2)(n+1)=56), इसलिए \(8\cdot7=56\) से (n=6)। लगातार संख्याओं से तुलना करें।

Open Question Page

Question 131/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{9!}{6!\cdot3!}\) का मान क्या है?

What is the value of \(\frac{9!}{6!\cdot3!}\)?

Explanation opens after your attempt

Correct Answer

C. (84)

Step 1

Concept

\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.

Step 2

Why this answer is correct

The correct answer is C. (84). \(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.

Step 3

Exam Tip

\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\) होता है। पहले (6!) काटने से हल छोटा होता है।

Open Question Page

Question 132/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{6!}{4!}-2!\) का मान क्या है?

What is the value of \(\frac{6!}{4!}-2!\)?

Explanation opens after your attempt

Correct Answer

B. (28)

Step 1

Concept

\(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.

Step 2

Why this answer is correct

The correct answer is B. (28). \(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.

Step 3

Exam Tip

\(\frac{6!}{4!}=30\) और (2!=2), इसलिए मान (28) है। भाग और घटाव का क्रम ध्यान रखें।

Open Question Page

Question 133/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+1)!}{(n-1)!}) किसके बराबर है?

(\frac{(n+1)!}{(n-1)!}) is equal to which expression?

Explanation opens after your attempt

Correct Answer

B. (n(n+1))

Step 1

Concept

((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).

Step 2

Why this answer is correct

The correct answer is B. (n(n+1)). ((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).

Step 3

Exam Tip

((n+1)!=(n+1)n(n-1)!) होता है। इसलिए भाग देने पर (n(n+1)) मिलता है।

Open Question Page

Question 134/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{4!\cdot5}{5!}\) का मान क्या है?

What is the value of \(\frac{4!\cdot5}{5!}\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

Since \(5!=5\cdot4!\), \(\frac{4!\cdot5}{5!}=1\). Write a factorial using the nearest smaller factorial.

Step 2

Why this answer is correct

The correct answer is A. (1). Since \(5!=5\cdot4!\), \(\frac{4!\cdot5}{5!}=1\). Write a factorial using the nearest smaller factorial.

Step 3

Exam Tip

क्योंकि \(5!=5\cdot4!\), इसलिए \(\frac{4!\cdot5}{5!}=1\)। फैक्टोरियल को निकट छोटे फैक्टोरियल से लिखें।

Open Question Page

Question 135/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(3!\cdot4!\) का मान क्या है?

What is the value of \(3!\cdot4!\)?

Explanation opens after your attempt

Correct Answer

C. (144)

Step 1

Concept

(3!=6) and (4!=24), so the product is (144). Memorize small factorials.

Step 2

Why this answer is correct

The correct answer is C. (144). (3!=6) and (4!=24), so the product is (144). Memorize small factorials.

Step 3

Exam Tip

(3!=6) और (4!=24), इसलिए गुणनफल (144) है। छोटे फैक्टोरियल याद रखें।

Open Question Page

Question 136/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{8!}{5!\cdot3!}\) का मान क्या होगा?

What is the value of \(\frac{8!}{5!\cdot3!}\)?

Explanation opens after your attempt

Correct Answer

C. (56)

Step 1

Concept

\(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\). Cancel the common factorial first.

Step 2

Why this answer is correct

The correct answer is C. (56). \(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\). Cancel the common factorial first.

Step 3

Exam Tip

\(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\) होता है। पहले समान फैक्टोरियल काटें।

Open Question Page

Question 137/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (n!=120) हो, तो ((n-2)!) का मान क्या है?

If (n!=120), what is the value of ((n-2)!)?

Explanation opens after your attempt

Correct Answer

C. (6)

Step 1

Concept

(120=5!), so (n=5) and ((n-2)!=3!=6). Identify (n) first.

Step 2

Why this answer is correct

The correct answer is C. (6). (120=5!), so (n=5) and ((n-2)!=3!=6). Identify (n) first.

Step 3

Exam Tip

(120=5!), इसलिए (n=5) और ((n-2)!=3!=6)। पहले (n) पहचानें।

Open Question Page

Question 138/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{7!}{3!\cdot4!}\) का मान क्या है?

What is the value of \(\frac{7!}{3!\cdot4!}\)?

Explanation opens after your attempt

Correct Answer

C. (35)

Step 1

Concept

\(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\). Cancel (4!) and calculate.

Step 2

Why this answer is correct

The correct answer is C. (35). \(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\). Cancel (4!) and calculate.

Step 3

Exam Tip

\(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\) होता है। (4!) काटकर गणना करें।

Open Question Page

Question 139/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{5!}{2!}+1!\) का मान क्या है?

What is the value of \(\frac{5!}{2!}+1!\)?

Explanation opens after your attempt

Correct Answer

C. (61)

Step 1

Concept

\(\frac{5!}{2!}=60\) and (1!=1), so the value is (61). Both (1!) and (0!) equal (1).

Step 2

Why this answer is correct

The correct answer is C. (61). \(\frac{5!}{2!}=60\) and (1!=1), so the value is (61). Both (1!) and (0!) equal (1).

Step 3

Exam Tip

\(\frac{5!}{2!}=60\) और (1!=1), इसलिए मान (61) है। (1!) और (0!) दोनों (1) होते हैं।

Open Question Page

Question 140/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The first term is (n+2) and the second is (n), so the difference is (2). Simplifying separately reduces mistakes.

Step 2

Why this answer is correct

The correct answer is B. (2). The first term is (n+2) and the second is (n), so the difference is (2). Simplifying separately reduces mistakes.

Step 3

Exam Tip

पहला पद (n+2) और दूसरा (n) है, इसलिए अंतर (2) है। अलग-अलग सरलीकरण करने से गलती कम होती है।

Open Question Page

Question 141/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

किस मान के लिए ((n-3)!) परिभाषित होगा, यदि (n) पूर्णांक है?

For which value will ((n-3)!) be defined if (n) is an integer?

Explanation opens after your attempt

Correct Answer

C. (n=3)

Step 1

Concept

Factorial is defined for non-negative integers, so \(n-3\ge0\). Among the given options, (n=3) is correct.

Step 2

Why this answer is correct

The correct answer is C. (n=3). Factorial is defined for non-negative integers, so \(n-3\ge0\). Among the given options, (n=3) is correct.

Step 3

Exam Tip

फैक्टोरियल गैर-ऋणात्मक पूर्णांक के लिए परिभाषित होता है, इसलिए \(n-3\ge0\)। दिए विकल्पों में (n=3) सही है।

Open Question Page

Question 142/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{9!}{8!}+\frac{6!}{5!}\) का मान क्या है?

What is the value of \(\frac{9!}{8!}+\frac{6!}{5!}\)?

Explanation opens after your attempt

Correct Answer

C. (15)

Step 1

Concept

\(\frac{9!}{8!}=9\) and \(\frac{6!}{5!}=6\), so the sum is (15). Reduce simple ratios quickly.

Step 2

Why this answer is correct

The correct answer is C. (15). \(\frac{9!}{8!}=9\) and \(\frac{6!}{5!}=6\), so the sum is (15). Reduce simple ratios quickly.

Step 3

Exam Tip

\(\frac{9!}{8!}=9\) और \(\frac{6!}{5!}=6\), इसलिए योग (15) है। सरल अनुपातों को तुरंत घटाएं।

Open Question Page

Question 143/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(2!\cdot3!+4!\) का मान क्या है?

What is the value of \(2!\cdot3!+4!\)?

Explanation opens after your attempt

Correct Answer

B. (36)

Step 1

Concept

\(2!\cdot3!=2\cdot6=12\) and (4!=24), so the total is (36). Do multiplication before addition.

Step 2

Why this answer is correct

The correct answer is B. (36). \(2!\cdot3!=2\cdot6=12\) and (4!=24), so the total is (36). Do multiplication before addition.

Step 3

Exam Tip

\(2!\cdot3!=2\cdot6=12\) और (4!=24), इसलिए कुल (36) है। गुणा को जोड़ से पहले करें।

Open Question Page

Question 144/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+3)!}{n!}) का पूर्ण विस्तार कौन सा है?

Which is the complete expansion of (\frac{(n+3)!}{n!})?

Explanation opens after your attempt

Correct Answer

C. ((n+3)(n+2)(n+1))

Step 1

Concept

((n+3)!=(n+3)(n+2)(n+1)n!). After canceling (n!), three factors remain.

Step 2

Why this answer is correct

The correct answer is C. ((n+3)(n+2)(n+1)). ((n+3)!=(n+3)(n+2)(n+1)n!). After canceling (n!), three factors remain.

Step 3

Exam Tip

((n+3)!=(n+3)(n+2)(n+1)n!) होता है। इसलिए (n!) कटने पर तीन गुणनखंड बचते हैं।

Open Question Page

Question 145/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{10!}{7!\cdot3!}\) का मान क्या है?

What is the value of \(\frac{10!}{7!\cdot3!}\)?

Explanation opens after your attempt

Correct Answer

D. (120)

Step 1

Concept

\(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\). Reduce the large factorial to three factors.

Step 2

Why this answer is correct

The correct answer is D. (120). \(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\). Reduce the large factorial to three factors.

Step 3

Exam Tip

\(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\) होता है। बड़े फैक्टोरियल को तीन पदों तक घटाएं।

Open Question Page

Question 146/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{6!-5!}{4!}\) का मान क्या होगा?

What is the value of \(\frac{6!-5!}{4!}\)?

Explanation opens after your attempt

Correct Answer

C. (25)

Step 1

Concept

\(6!-5!=6\cdot5!-5!=5\cdot5!\), and \(\frac{5\cdot5!}{4!}=25\). Take the common factorial first.

Step 2

Why this answer is correct

The correct answer is C. (25). \(6!-5!=6\cdot5!-5!=5\cdot5!\), and \(\frac{5\cdot5!}{4!}=25\). Take the common factorial first.

Step 3

Exam Tip

\(6!-5!=6\cdot5!-5!=5\cdot5!\), और \(\frac{5\cdot5!}{4!}=25\)। पहले सामान्य फैक्टोरियल निकालें।

Open Question Page

Question 147/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+2)!+(n+1)!}{(n+1)!}) का सरल रूप क्या है?

What is the simplified form of (\frac{(n+2)!+(n+1)!}{(n+1)!})?

Explanation opens after your attempt

Correct Answer

B. (n+3)

Step 1

Concept

((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!). Therefore the value is (n+3).

Step 2

Why this answer is correct

The correct answer is B. (n+3). ((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!). Therefore the value is (n+3).

Step 3

Exam Tip

((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!)। इसलिए मान (n+3) है।

Open Question Page

Question 148/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

\(\frac{12!}{9!}\) में कितने लगातार गुणनखंड बचते हैं?

How many consecutive factors remain in \(\frac{12!}{9!}\)?

Explanation opens after your attempt

Correct Answer

B. (3)

Step 1

Concept

\(\frac{12!}{9!}=12\cdot11\cdot10\), so three factors remain. Cancel the numerator up to the denominator factorial.

Step 2

Why this answer is correct

The correct answer is B. (3). \(\frac{12!}{9!}=12\cdot11\cdot10\), so three factors remain. Cancel the numerator up to the denominator factorial.

Step 3

Exam Tip

\(\frac{12!}{9!}=12\cdot11\cdot10\), इसलिए तीन गुणनखंड बचते हैं। हर के फैक्टोरियल तक अंश को काटें।

Open Question Page

Question 149/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

यदि (r!=24) हो, तो ((r+1)!) का मान क्या होगा?

If (r!=24), what will be the value of ((r+1)!)?

Explanation opens after your attempt

Correct Answer

D. (120)

Step 1

Concept

(24=4!), so (r=4) and ((r+1)!=5!=120). First find the variable from the given factorial.

Step 2

Why this answer is correct

The correct answer is D. (120). (24=4!), so (r=4) and ((r+1)!=5!=120). First find the variable from the given factorial.

Step 3

Exam Tip

(24=4!), इसलिए (r=4) और ((r+1)!=5!=120)। पहले दिए फैक्टोरियल से चर का मान निकालें।

Open Question Page

Question 150/150 Medium Mathematics Permutations and Combinations Factorial notation Class 11 Level 57

(\frac{(n+1)!}{(n+1)n!}) का मान क्या है?

What is the value of (\frac{(n+1)!}{(n+1)n!})?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

((n+1)!=(n+1)n!), so the whole fraction becomes (1). Remembering this identity saves time.

Step 2

Why this answer is correct

The correct answer is B. (1). ((n+1)!=(n+1)n!), so the whole fraction becomes (1). Remembering this identity saves time.

Step 3

Exam Tip

((n+1)!=(n+1)n!), इसलिए पूरी भिन्न (1) बनती है। पहचान सूत्र याद रखने से समय बचता है।

Open Question Page

Class 11 Mathematics - Permutations And Combinations - Factorial notation Medium Quiz

यदि (\frac{(n+1)!}{n!}=8), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{9!}{7!}-5!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (n=3), तो (\frac{(n+2)!}{n!}) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि ((n+1)!=720), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{6!}{3!}+4!\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{5!}{3!}+\frac{5!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!}) का सरल मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{n!}{(n-2)!}=42), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{10!}{8!}+\frac{4!}{2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{7!-6!}{6!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(\frac{(n+3)!}{n!}) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{(n+2)!}{n!}=30), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{5!+3!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{8!}{4!}-\frac{7!}{4!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{11!}{9!,2!}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

कौन सा रूप \(\frac{12!}{9!}\) के बराबर है?

Concept

Why this answer is correct

Exam Tip

(\frac{(n+1)!-n!}{n!}) का सरल रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (\frac{n!}{(n-1)!}+2=9), तो (n) का मान क्या है?

Concept

Why this answer is correct